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<h3 class="heading"><span class="type">Paragraph</span></h3>
<p>Recall from calculus that a power series in <span class="process-math">\(x-x_0\)</span> is an infinite series of the form</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
\sum_{n=0}^{\infty} a_n(x - x_0)^n=a_0 + a_1(x-x_0)+a_2(x-x_0)^2+\cdots
\end{equation*}
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<p class="continuation">Such a series is also said to be a <dfn class="terminology">power series centered at <span class="process-math">\(x_0\)</span></dfn>. For example, the power series <span class="process-math">\(\sum_{n=0}^{\infty}(x+1)^n\)</span> is centered at <span class="process-math">\(x_0=-1\text{.}\)</span>The following list summarizes some important facts about power series.</p>
<span class="incontext"><a href="sec5_1.html#p-175" class="internal">in-context</a></span>
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